How Do Charge and Mass Affect Ion Acceleration in an Electric Field?

[mpswee2]

Homework Statement

Assuming equal masses, how would the detection times of 3H+ and 3He+ compare [as they're both accelerated toward a detector in the direction of a constant E field]?

A) 3H+ would have a longer flight time than 3He+.

B) 3H+ would have a shorter flight time than 3He+.

C) 3H+ would have the same flight time as 3He+.

D) The radioactive 3H+ would always decay before detection.

Homework Equations

Now, I initially thought it was C: both would have the same flight time since they have equal masses and, therefore, equal velocities once PE (PE=QV) is completely converted to kinetic energy (v= sqrt(2KE/m)).

But I realized-- in an 'aha!' moment-- that, although they have equal masses, they have UNequal charge, Q. The helium ion has 2 protons and 1 e-, while the H+ ion has 1 proton and no e-. If the Q of He+ and H+ are not equal, their initial PE = QV will not be equal, so their KE will not be equal. Because He+ has a higher Q due to 2 protons, the He+ has higher initial PE and greater KE after acceleration. It's flight time to reach detector should be less (ie faster travel) than H+, which has less KE.

But C was the correct answer. Could someone point out where my reasoning is flawed? Apparently He+ and H+ have equal Q-values. Is this because they're both +1 cations? Does the ionic charge alone always tell us a particle's charge? As I understood, simply losing 1 e- (to form +1 cation) won't always equalize the charges between ions due to differential number of protons. The additional protons in He+ should account for a different (greater) overall Q compared to in H+-- no??

I guess, in the end, I'm curious how you determine an ions Q. Is Q always going to equal the overall ionic charge-- or do we need to take the number of protons into account when we have ions with equal charges?

Thanks a lot.

The Attempt at a Solution

 

[Dick]

3H+ has two neutrons, one proton and no electrons. 3He+ has two protons, one neutron and one electron. The net charge of both is the same, +1. The masses are almost (but not exactly) equal - but you are told to assume they are. Hence, C. The '+' symbol is indicating total charge.